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Universal gas constant (J mol −1 ☌ −1) Re Heat transfers from the membrane surface to permeate side through the membrane (W m −2) r Heat transfers from the bulk solution to the membrane surface through the boundary layer (W m −2) Q m Mass transfer coefficient across the membrane pores (kg m −2 s −1 Pa −1) M Solute mass transfer coefficient across thermal boundary layer (m s −1) K m Heat transfer coefficient at the feed solution boundary layer (W m −2 ☌ −1) i

Heat capacity of feed solution (kJ kg −1 ☌ −1) dĭiffusion coefficient of the solute in solvent (m 2 s −1) e 1, e 2, e 3, e 4

Heat transfer area of heat exchanger (m 2) A f Therefore, these results can provide significant references for the implementation and further optimization of the proposed system in the future. Eventually, an economic evaluation of the proposed system is performed comprehensively and the most optimized compression ratio of compressor can be obtained, which can guarantee the lowest energy consumption and total annual cost.

Compared with the conventional VMD system and multi-effect MD system, the proposed system can save 77.6% and 20.4% energy due to a significant improvement in thermal efficiency by recovering the latent heat of vaporization.

Furthermore, the energy consumption of the proposed system is explored through analyzing the influences from key factors, including boiling point elevation, temperature and concentration polarization and heat transfer temperature difference of heat exchanger on power consumption of compressor. The membrane flux increases with the increase in feed temperature and velocity, but it decreases with the increase in feed concentration and permeate-side absolute pressure. The influences of the corresponding operating parameters including feed concentration, feed temperature, feed velocity and permeate-side absolute pressure on membrane flux are investigated and discussed. This paper presents a new vacuum membrane distillation (VMD) coupled with mechanical vapor recompression system for the concentration of sulfuric acid solution the mathematical models based on the mass and energy balances in each part of the system are established.